How do you order two numbers written in scientific notation? - Answers

If the signs at the front of the numbers are different then the one with the negative sign is smaller. So the question can be simplified to ordering two numbers that have the same sign. Suppose they are both positive numbers. If one of them has a smaller exponent (power of 10) than the other, then that number is smaller. That then leaves two positive numbers with the same exponent. So the only difference is in the mantissa (or the bit before the power of 10). Since the powers of 10 are the same in both cases, the smaller mantissa gives the smaller number. Going back to the case where both numbers are negative: their ordering is the same as for negative integers, for example. The bigger absolute value gives the smaller negative number.